Let x be the required Arithmetic Mean,then if 8, x, 16 form three successiveterms in the Aritmetic Progression,x is

Answer:The middle term in the sequence is 12.Arithmetic mean of the sequence is x  = 12 Step-by-step explanation:Here, three consecutive terms in the AP  are 8 , x , 16.Now, if and three a, b , c terms are in an arithmetic progression.⇒  b -a  =  Common difference (d)   = c - bSimilarly here, 8 , x , 16 are in AP.⇒   x  - 8  =  16 - x  = Common difference dor, x + x  = 16 + 8 or, 2 x = 24⇒  x =  24/2    = 12or , x   = 12Hence, the middle term in the sequence is 12. Also, arithmetic mean of 8, 12, 16  = [tex]\frac{\textrm{Sum of observations}}{\textrm{Number of observations}}[/tex]⇒ [tex]\frac{8+ 12+ 16}{3}   = \frac{36}{3} = 12[/tex]Arithmetic Mean  = 12